A Dynamic Control Model for Managing Bus Bunching Problem with Capacity Constraints

Bus bunching is a critical issue in urban transit systems. It can lead to increased transit cost for passengers and uneven passenger loads among transit vehicles. Bus bunching problem can be formulated into two types of optimization problems. The first type is to use the total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies feedback control framework to minimize the headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are suitable for real-time transit operations. The headway-based feedback control framework proposed in existing literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study providesthe stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with numerical analysis and a case study based on field data collected in Chengdu, China. The results show that the proposed model performs well in high-demand bus routes.